where \(T_\alpha = \tilde{t}(\varphi _0(\alpha ),Y(\varphi _0(\alpha ),\alpha ),\alpha ,0)\)  is the period associated to the limit cycle \(\Gamma _\alpha \subset \mathcal {M}\)  of the layer problem (REF ) which passes through the point \((\varphi _0(\alpha ), Y(\varphi _0(\alpha ),\alpha ), \alpha ) \in S_\Delta \) . In classical averaging theory, the integral (REF ) defines the so-called averaged equation [1]}, [2]}.

